Which of the following numbers is a multiple of 13? ${40,65,86,97,115}$
Explanation: The multiples of $13$ are $13$ $26$ $39$ $52$ ..... In general, any number that leaves no remainder when divided by $13$ is considered a multiple of $13$ We can start by dividing each of our answer choices by $13$ $40 \div 13 = 3\text{ R }1$ $65 \div 13 = 5$ $86 \div 13 = 6\text{ R }8$ $97 \div 13 = 7\text{ R }6$ $115 \div 13 = 8\text{ R }11$ The only answer choice that leaves no remainder after the division is $65$ $ 5$ $13$ $65$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $13$ are contained within the prime factors of $65$ $65 = 5\times13 13 = 13$ Therefore the only multiple of $13$ out of our choices is $65$. We can say that $65$ is divisible by $13$.